The resolution limits of tape head lateral position estimates derived from timing-based servo (TBS) patterns preformatted on perpendicularly oriented barium ferrite tape media are investigated. A set of four new TBS patterns with azimuth angles ranging from 15° to 24° but having, otherwise, identical parameters are compared. Measurements of the standard deviation of the closed-loop position-error signal are compared with resolution estimates based on: 1) the noise floor of the power spectral density of the lateral tape motion measured from the servo pattern during open or closed-loop track-following and 2) an analytical lower bound on the mean-squared estimation error, which depends on the servo readback signal shape and the signal-to-noise ratio. All four servo patterns are shown to achieve nanoscale resolution under realistic operating conditions. The 24° pattern was found to provide the highest performance with a position estimation resolution better than 3.8 nm for a single channel, and better than 2.6 nm when the estimates of two channels are combined.